# How do you find the absolute value of #10-7i#?

##### 1 Answer

#### Explanation:

The **absolute value** of a number is better thought of as the distance that number is from the origin. For numbers in

Since we use a 2-D plane to illustrate complex numbers, we will use the formula for the 2-D distance

#d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

This can be simplified further for the use of absolute values, since the first point will always be the origin

#d=sqrt((x_2-0)^2+(y_2-0)^2)#

#color(white)d=sqrt(x_2^2+y_2^2)#

or simply

#abs[(x, y)# #=sqrt(x^2+y^2)#

A complex number

That means the distance that a number

#abs((a+bi))=sqrt(a^2+b^2)#

For the complex number

#abs((10-7i))=sqrt(10^2+("-7")^2)#

#color(white)(abs((10-7i)))=sqrt(100+49)#

#color(white)(abs((10-7i)))=sqrt(149)" "approx 12.21# .